Mini Exam 27 — Timed Mini Exams

Questions in this quiz (10)

1. If $$|k-5|\le8$$, which of the following CANNOT be the value of $$k$$?

   • $$8$$
   • $$5$$
   • $$-3$$
   • $$-4$$

2. In the figure above, $$k$$ is a positive number. If the area of $$\triangle PQR$$ is $$12$$, what is the value of $$k$$?

   • $$2$$
   • $$2\sqrt2$$
   • $$4$$
   • $$4\sqrt2$$

3. If $$x$$, $$y$$, and $$z$$ are positive and $$\frac{x^2y^{-3}}{z^2}=9y,$$ which of the following is equal to $$x^{-1}$$?

   • $$\frac{1}{3y^2z}$$
   • $$\frac{3z}{2}$$
   • $$\frac{1}{3z}$$
   • $$\frac{yz}{3}$$

4. Allen and Barbara leave their house at the same time. Allen walks due east for $$3$$ hours and due north for $$3\frac{1}{2}$$ hours at the average rate of $$2$$ kilometers per hour, and Barbara walks due south for $$3$$ hours and due west for $$2$$ hours at the average rate of $$3$$ kilometers per hour. At the end of their walk, what is the straight-line distance between them, in kilometers?

   • $$25$$
   • $$20$$
   • $$8\sqrt2$$
   • $$6\sqrt2$$

5. In the figure above, line $$\ell$$ is parallel to line $$m$$. What is the value of $$x$$?

   • $$40^\circ$$
   • $$50^\circ$$
   • $$60^\circ$$
   • $$80^\circ$$

6. Let the function $$f$$ be defined by $$f(x)=x-p$$. If $$f(2)=-1$$, what is the value of $$f(2p)$$?

   • 3

7. In the figure above, a circle is tangent to the line at point $$P$$. If the radius of the circle is $$5$$, what is the value of $$t$$, the $$y$$-intercept of the line?

   • $$-\frac{3}{4}$$
   • $$\frac{4}{3}$$
   • $$\frac{9}{4}$$
   • $$\frac{25}{4}$$

8. In the figure above, the graph of $$y=f(x)$$ is shown in $$-4\le x\le4$$. If $$f(k)=3$$, how many values of $$k$$ are there in the interval?

   • $$0$$
   • $$1$$
   • $$2$$
   • $$3$$

9. The profit, $$p$$, in dollars, from a car wash is given by the function $$p(x)=\frac{50x-200}{x}+k,$$ where $$x$$ is the number of cars washed and $$k$$ is a constant. If $$20$$ cars were washed today for a total profit of $$300$$, what is the value of $$k$$?

   • $$100$$
   • $$200$$
   • $$260$$
   • $$300$$

10. In the figure above, $$ABCD$$ is a rectangle and $$BM$$ is perpendicular to $$AC$$. If the length of $$AM$$ is $$2$$ and the length of $$CM$$ is $$18$$, what is the area of $$\triangle ABC$$?

    • $$40$$
    • $$60$$
    • $$80$$
    • $$100$$